# Maximum Distance? 1d Kinematics

• Kildars
In summary, the maximum possible value for d, in meters, is 72. This is the distance the tourist can safely run before getting caught by the bear.
Kildars
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.5 m/s. The car is a distance d away. The bear is 24 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

In meters.

I know the bear is at D+24.. I don't really know how to start this though.

Set up equations for the positions at any time t for the tourist and bear:

$$x_{tourist}(t)=d-4.5t$$

$$x_{bear}(t)=(d+24)-6.0t$$

Now if you equate the two equations, you can find how long it takes for the bear to catch the tourist (when their positions are equal):

$$d-4.5t=d+24-6t \implies 1.5t=24 \implies t=16s$$

So the most time the tourist can run before getting caught is 16s, and since he is moving at 4.5m/s he goes a distance of 72m before getting caught. So the maximum of d is 72, or else the tourist will get caught.

Cheers,
Josh

Thank you Josh, I understand now.

The "extreme case" is when the bear and the tourist reach the car at the same time. This happens when the bear reaches the car in the same time that the tourist reaches the car. The toursist takes a time $\Delta t = D/4.5$ to reach the car. So you want to use the equation of kinematics

$$x(t)=x_0+v_0\Delta t$$

for the motion of the bear in the case where the bear reaches the car in a time $\Delta t = D/4.5$, and solve for D.

## What is "Maximum Distance" in 1d Kinematics?

Maximum distance is the farthest distance that an object can travel in one dimension (such as left or right) without changing direction. It is a measure of the object's displacement.

## How is "Maximum Distance" calculated in 1d Kinematics?

To calculate maximum distance, you need to know the initial velocity, acceleration, and time. It can be calculated using the formula: d = v0t + 1/2at^2, where d is the maximum distance, v0 is the initial velocity, a is the acceleration, and t is the time.

## What is the difference between "Maximum Distance" and "Total Distance" in 1d Kinematics?

Maximum distance only accounts for the farthest distance an object can travel in one direction, while total distance takes into account the distance traveled in both directions. Total distance can be calculated by adding up the maximum distance in each direction.

## Can the "Maximum Distance" be negative in 1d Kinematics?

Yes, the maximum distance can be negative if the object is moving in the negative direction (e.g. left) with a negative velocity. This indicates that the object has traveled backwards from its starting point.

## How can "Maximum Distance" be applied in real-life situations?

Maximum distance in 1d Kinematics can be applied in a variety of real-life situations, such as calculating the maximum distance a car can travel before coming to a complete stop, or the maximum distance a projectile can travel before hitting the ground. It is also useful in analyzing the motion of objects in sports, such as the maximum distance a baseball can be hit or the maximum distance a javelin can be thrown.

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